# Find the location of the aerodynamic center.

An airfoil has a lift coefficient and moment coefficient of $$-0.35$$ and $$-0.050$$ about quarter-chord at $$-6^{\circ}$$ angle of attack. The airfoil has lift coefficient and moment coefficient of $$0.70$$ and $$-0.040$$ at an angle of attack of $$4^{\circ}$$ about the same quarter chord. Find the location of the aerodynamic center.

Asked on 22nd July 2021 in

Aerodynamic center is a point on the airfoil for which the aerodynamically generated moment is independent of the angle of attack or the coefficient of lift. Aerodynamic center is at $$\frac{1}{4}$$ chord from the leading edge for most of the low speed airfoils. For supersonic airfoils aerodynamic center lies nearer at $$\frac{1}{2}$$ chord length. Location of the aerodynamic center as a fraction of the chord length is given as $x_{ac}=-\frac{m_{0}}{a_{0}}+0.25$$$m_{0}$$ = Slope of the moment coefficient curve, $m_{0}=\frac{-0.040-\left ( -0.050 \right )}{4^{\circ}-\left ( -6^{\circ} \right )}=0.001\textrm{ per degree}$ $$a_{0}$$ = Slope of the lift coefficient curve, $a_{0} = \frac{0.70-\left ( -0.35 \right )}{4^{\circ}-\left ( 6^{\circ} \right )} = 0.105 \textrm{ per degree}$Therefore, aerodynamic center lies at,$x_{ac} = -\frac{m_{0}}{a_{0}} + 0.25$$\Rightarrow x_{ac} = -\frac{0.001}{0.105} + 0.25 = 0.240 \textrm{ chord length}$